Logistic Regression: "Logistic Regression (SGD)
Logistic regression is a model used for prediction of the probability of occurrence of an event. It makes use of several predictor variables that may be either numerical or categories.

Logistic regression is the standard industry workhorse that underlies many production fraud detection and advertising quality and targeting products. The Mahout implementation uses Stochastic Gradient Descent (SGD) to all large training sets to be used.

For a more detailed analysis of the approach, have a look at the thesis of Paul Komarek:

Logistic: "
In order to find the matrix B for which L is minimised, a Quasi-Newton Method is used to search for the optimized values of the m*(k-1) variables. Note that before we use the optimization procedure, we 'squeeze' the matrix B into a m*(k-1) vector. For details of the optimization procedure, please check weka.core.Optimization class.

Although original Logistic Regression does not deal with instance weights, we modify the algorithm a little bit to handle the instance weights.